Best Known (31, 31+30, s)-Nets in Base 2
(31, 31+30, 23)-Net over F2 — Constructive and digital
Digital (31, 61, 23)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 20, 9)-net over F2, using
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 5 and N(F) ≥ 9, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (5, 8)-sequence over F2, using
- digital (11, 41, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- digital (5, 20, 9)-net over F2, using
(31, 31+30, 27)-Net over F2 — Digital
Digital (31, 61, 27)-net over F2, using
- net from sequence [i] based on digital (31, 26)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 31 and N(F) ≥ 27, using
(31, 31+30, 75)-Net over F2 — Upper bound on s (digital)
There is no digital (31, 61, 76)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(261, 76, F2, 30) (dual of [76, 15, 31]-code), but
(31, 31+30, 76)-Net in Base 2 — Upper bound on s
There is no (31, 61, 77)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(261, 77, S2, 30), but
- the linear programming bound shows that M ≥ 1134 474760 533137 424384 / 437 > 261 [i]